Diffraction

PHYS261 fall 2006

• Diffraction is a phenomenon when a wave that passes through an aperture or around an obstacle forms a pattern on a screen.

• What causes diffraction is interference of an infinite number of waves that are emitted by the points of the aperture

• Huygens principle says that a large hole can be approximated by many small holes where each are a point source.

• The point source generating spherical waves is the source of diffraction.

• There are two different limiting types of diffraction observations

- Fresnel diffraction patterns- Fraunhofer diffraction patterns

Fresnel cases: quadratic dependence on the distance from the normal (from the "axis" or "the edge")

Fraunhofer cases: large distance; the quadratic term becomes negligible, the linear is important

Formulas discussed later

• For Fraunhofer diffraction pattern there is a large distance between aperture and the screen.

• For Fresnel diffraction the distance between the aperture and the screen is generally small.

The field generated by the source is propa-

gating towards an aperture and there will be

diffraction through the aperture.

The figure shows a bending of light around

a circular aperture:

Example of Fresnel diffraction

Example of Fresnel diffraction

theta and l the wavelength lambda) then the Airy disk has its first minimum.

D is the diameter of the aperture.

Fraunhofer diffraction.

Airy disk: This is a Fraunhofer diffraction.

• At a circular aperture the intensity pattern is called an Airy disk.

• It is a ring system so that the plots are radial sections of a pattern possesing circular symmetry. When theta = 1.22 lambda/D ( theta should equal the angle theta and l the

wavelength lambda) then the Airy disk has its first minimum.)

Fraunhofer diffraction.

Example of Fresnel diffraction at straight edge:

• The intensity distribution shows that at the

edge the intensity of the light is reduced to

a quarter of the intensity and behind the edge it is falling monotonically to zero.

Outside the intensity is increasing and it oscillates with increasing frequency.

Fresnel diffraction at straight edge: